The objective of the study is to develop statistical procedures that aid the planning and analysis of animal bioassays run over time that concern the time elapsed before an outcome. Time may be directly observable (survival time) or may be estimated (time- to-tumor) by observing the presence or absence of tumors. The research will determine how many animals are needed in a bioassay to attain a given power to detect dose response relationships, allowing possibly for serial sacrifice during the experiment. The proposed method is expected to be superior to other approaches since it makes no specific assumptions on the rate of tumor development, and views the number of animals at risk at a given time as a random variable rather than a fixed quantity. Linear rank statistics for tumorigenicity experiments will be developed to compare control and exposed groups of animals with respect to the prevalence of nonlethal types of tumors, detectable only at death or sacrifice. It is anticipated that the procedure will be computationally more efficient than those in current use, thus making it easier to detect agents that increase the prevalence of such tumors. A test for trend in teratological data will be developed based on the C alpha test, will be applied to existing data sets, and compared to other procedures. Such a test is required since methods that ignore litter effects may be misleading, and the proposed test may be superior to other procedures since it is base on optimality criteria. Tests for litter effects will be developed based on observations at several sites, and our previously developed tests for such effects will be made more robust.